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We present an adjoint-based method for the calculation of eigenvalueperturbations in nonlinear, degenerate and non self-adjoint eigenproblems. Thismethod is applied to a thermo-acoustic annular combustor network, the stabilityof which is governed by a nonlinear eigenproblem. We calculate the first- andsecond-order sensitivities of the growth rate and frequency to geometric, flowand flame parameters. Three different configurations are analysed. Thebenchmark sensitivities are obtained by finite difference, which involvessolving the nonlinear eigenproblem at least as many times as the number ofparameters. By solving only one adjoint eigenproblem, we obtain thesensitivities to any thermo-acoustic parameter, which match thefinite-difference solutions at much lower computational cost.

Stability analysis of thermo-acoustic nonlinear eigenproblems in annular combustors. Part I. Sensitivity